ࡱ> j'` bjbj UO^ & & & & JZJZJZ8ZtZ46]h_4___CbCbCb||||G|((E$:hi&c!b"Cb&c&ci& & __O>ggg&c& D__|g&c|ggo|j Dp_*] @I=!TJZdoxq4 T0oZVelV$pVpxCb"ebg}bbCbCbCbii@gvCbCbCb&c&c&c&c$JXdX& & & & & &  Solutions: Third Group Finance-Moeller Remember: Rounding on larger problems like WACC calculation will lead to slightly different results. When I do my calculations I do the computations in Excel with retain the full precision of the numbers. 1. a. If BIT intends to keep its borrowing permanently at this level, the interest tax shield will be received in perpetuity. Therefore, the perpetuity formula can be used to value it.  EMBED Equation.3  EMBED Equation.3  Since most of BITs debt is floating rate, we can assume that the firms interest cost is also the cost of debt. In this case C = the interest tax shield = 0.35 * $387.5 million * 0.08 = $10,850,000. Since we believe we will always be able to use the interest tax shield (implies little risk on this dimension) and the dollars of debt will be constant the appropriate degree of riskiness for the NPV of financing/capital structure (D), will be the return on debt, 8%.  EMBED Equation.3  b. To find the cost of equity of this firm we first need to determine what relationship (Case 1, Case 2 or Case 3) to use. In part (a) we have already decided that the appropriate riskiness of D is the cost of debt so that leaves either Case 2 or Case 3. So the question is, can we assume that D=tD? Again from part (a) it seems this is a good assumption so we can use Case 3. Also remember that we can substitute in R for B in this equation.  SHAPE \* MERGEFORMAT   EMBED Equation.3  EMBED Equation.3  c. With the suggested shift in BITs capital structure policy, Case 3 is no longer the appropriate assumption. This policy shift to a constant proportion of debt implies that the riskiness of D is closer to the riskiness of assets, so Case 1 is the best choice.  EMBED Equation.3  d. The key to understanding this difference is in the assumption about the riskiness of D. Remember in the first scenario, the riskiness was similar to debt while in the second scenario it was similar to equity. Also, think of the value of the firm as the combination of the value of the assets (the economic function of the company) and the NPV of financing. So the change in the assumption about the riskiness of D, implies that the overall riskiness of the firm has changed because the NPV of financing has changed. To get a sense of the magnitude of this change, think about how much of the value of the firm is based on the capital structure choice. In this case the overall value of the firm is $1,087.5 million (D+E=387.5+700) and the NPV of financing is $135.625, so financing accounts for approximately 12% (135/1087) of the value of the firm. When you change the riskiness of 12% of the firm from 8% (return of debt) to 12% (return of assets), you get a corresponding increase in the return of equity, 13.44% to 14.21%. 2. In a world with no taxes or bankruptcy costs, there are no advantages or disadvantages to issuing debt or equity. The only thing debt affects is the ownership structure of the firm. So, in a world with no taxes or bankruptcy costs, issuing debt does not affect the value of a firm. This is M&M proposition I. When a firm issues debt, more of the cash flows from the assets must go to paying the principal and interest on the debt. This makes it less likely that the equity holders will receive the cash flows that the assets generate. This will increase the risk to equity holders and the expected return on equity must increase to compensate them for this greater risk. Since the value of the firm is unaffected by the capital structure, it implies that the WACC for the firm is also unaffected. Also, with no taxes or bankruptcy costs, the WACC only reflects the operating or business risk of the firm's assets (or investment projects) and this risk is unaffected by the capital structure. As the debt to equity ratio increases, whatever equity is outstanding must absorb the fixed business risk of the firm. Therefore, as the leverage increases, the return on equity increases. (This is M&M proposition II.) 3. The goal is to estimate a return on assets (the business risk) of the similar publicly traded firm (un-lever) then add back the capital structure risk of your company (lever). To un-lever you need to determine what the riskiness of D is for the similar public company. Since this firm proclaims to keep a constant proportion of debt, you can assume the riskiness of the assets is similar to the riskiness of D, so you can use Case 1.  EMBED Equation.3  Now that you have the return on assets, you want to re-lever the business risk to your capital structure choice and compute the beta of equity. Since your company uses a constant proportion of debt, you can assume the riskiness of the assets is similar to the riskiness of D, so you can also use Case 1 for this step.  EMBED Equation.3  Now use the estimates of your betas to calculate the returns of debt and equity then plug those numbers into the WACC to get the appropriate r.  EMBED Equation.3   EMBED Equation.3  Now to calculate the NPV of the project you simply take the cost plus the perpetual cash flows discounted by the WACC. You should recommend that you accept the project because the NPV is greater than 0.  EMBED Equation.3  4. If the project is all equity financed your new r is just the return on equity for the project. Granted you could do the WACC calculation but since there is zero debt in the capital structure it will just be the return on equity. From the previous problem we know that the unlevered risk of this project is the beta of assets as estimated from the similar publicly traded firm or 1.36. We put this beta estimation into the CAPM, then discount the cash flows with this r.  EMBED Equation.3   EMBED Equation.3  If this project is all equity financed you would not do the project because the NPV is less than 0. 5. Once you have done the previous two NPV calculations, it is fairly easy to compute the value of the financing. For this project the value of the 75/25 capital structure is worth $8.95 million (5.36- -3.69). 6. In this scenario we do all the same steps as problem 3 with the only difference being that we estimate your companys return on equity using the assumption that the riskiness of the assets is similar to the riskiness of the NPV of financing, i.e. Case 3. Since there are no new assumptions about the industry, we can continue to use the Case 1 relationship to find the Ba for the industry. Identical to the computation in question 3, we find Ba by the following.  EMBED Equation.3  Then we take the industry revealed Ba, assume that your firms Ba will be similar and we re-lever to find your new Be.  EMBED Equation.3  Now plug the appropriate Bs into the CAPM to get the Rs.  EMBED Equation.3  Finally the final R is computed by using the WACC relationship.  EMBED Equation.3  Next we compute the NPV of the project with the new WACC.  EMBED Equation.3  The value of the NPV of financing in this case is the difference between $19.19 million and the all equity financed project computed in problem 4, -3.69. So the value of D is $22.88 million (19.19- -3.69). If you assume the riskiness of the NPV of financing is similar to the riskiness of debt (so the discount rate of the NPV of financing is Rd rather than Ra (in problem 3)), the value of the project increases. Correspondingly, the difference in the value of the financing/capital structure (D) between problem 5 and problem 6 is fully derived from the difference in your choice of R to discount the NPV of financing. 7a. Given the available information, you can estimate the cost of equity for XYZ by using the dividend growth model. Remember we know that analysts are typically optimists so Im going to divide the predicted growth rate by 2 to get something that is more historically accurate so g equals 10% (0.2/2).  EMBED Equation.3  b. Given the available information, you can estimate the return on debt by using the CAPM (basically as soon as you see a beta, you should think of the CAPM as a possibility). The CAPM shows that the Rd=0.03+0.5(0.1)=0.08 or 8%. 8. In this problem there are at least two ways to solve some of the missing items. No matter which way you choose, the answers should be the same. First find the appropriate proxies for the market value of the firms debt and equity. Below is a table with those numbers. The equity numbers are the shares outstanding times the stock price. The debt amount for the Domestic subsidiary is the market value that is given while the best proxy available for the International subsidiary is the book value. I have also included four rows of various percentages of Debt and Equity which we will use to do the calculations. NOPNOP InternationalNOP DomesticMkt Value of Equity753045Mkt Value of Debt25520E%(in firm)100%40%60%D%(in firm)100%20%80%E%(in division)75%85.71%69.23%D%(in division)25%14.26%30.77% NOPNOP InternationalNOP DomesticWACC0.12710.14750.1160Re0.15400.160.15Rd0.070.11000.06Bd0.40.80.3 First we can find the NOP Re by simply taking the weighted average of the two divisions Res. Since these are equity based returns, we should weight them by the %Equity in the firm (40% and 60%). NOP Re=0.4*0.16+0.6*0.15=0.1540. Next we can find Internationals Rd in a similar manner but we weight them by the %Debt in the firm. 0.07=0.2*International Rd + 0.8*0.06 Solving for International Rd we find it is 0.1100 or 11% Then we can solve for the three Bds by using the CAPM relationship and solving it for beta. Ri = (Rf + Bi (Rm-Rf) Bi = (Ri-Rf)/ (Rm-Rf) For instance for NOP, Bd = (0.07-0.03) / (0.1) = 0.4. Use the same method to solve for the two divisions. Note that you can check your calculations of the two divisions by making sure that the weighted average of them (using the %Debt in the firm) is equal to NOPs Bd. Last you can easily solve for the three WACCs by just using the traditional WACC equation and the in division weights.  EMBED Equation.3  Again, you can easily check this WACC by averaging the divisional WACCs by the overall value of the two divisions relative to the whole firm. 9. The interest reduced Nike's tax bill by $10,850,000. Thus, if the firm were entirely equity financed it would have had to pay $10,850,000 more in taxes. Since interest payments are tax deductible, the savings is calculated by taking the interest paid and multiplying it by the tax rate. $31,000,000 * 0.35 = $10,850,000 a. If Nike intends to keep its borrowing permanently at the present level, the interest tax shield will be received in perpetuity. Therefore, the perpetuity formula can be used to value it.  EMBED Equation.3  EMBED Equation.3  In this case C = the interest tax shield = 0.35 * $31 million = $10,850,000 R = the interest rate of 8%.  EMBED Equation.3  b. If Nike intended to eliminate all debt after one year, the interest tax shield will last for only one year. Its present value is.  EMBED Equation.3  10. a. Recall that:  EMBED Equation.3   EMBED Equation.3  Current Capital StructureEBIT $ 750,000  $ 1,125,000  $ 1,500,000 Interest -  -  - Net Income 750,000  1,125,000  1,500,000 Shares outstanding 400,000  400,000  400,000 EPS $ 1.88  $ 2.81  $ 3.75 Market value of equity $ 10,000,000  $ 10,000,000  $ 10,000,000 ROE7.5%11.3%15.0% b. Similarly, we can calculate the EPS and the ROE assuming the firm goes through with the proposed recapitalization. Proposed Capital StructureRecessionNormalExpansionEBIT $ 750,000  $ 1,125,000  $ 1,500,000 Interest (400,000) (400,000) (400,000)Net Income 350,000  725,000  1,100,000 Shares outstanding 240,000  240,000  240,000 EPS $ 1.46  $ 3.02  $ 4.58 Market value of equity $ 6,000,000  $ 6,000,000  $ 6,000,000  ROE5.8%12.1%18.3%c. The effects of leverage serve to magnify the gains and losses to shareholders by increasing the volatility of the EPS and the ROE. When the firm issues debt and buys back stock, there are fewer shares of stock outstanding. Therefore, the net income that the firm pays out will be spread across fewer stockholders and thus gains and losses to the shareholders are magnified for the levered firm. For a given increase in EBIT, the EPS for the proposed structure (levered firm) will increase by a greater percentage than the EPS of the current structure (unlevered firm). Conversely, if EBIT decreases, the EPS of the proposed structure will also fall by a larger percentage than the EPS of the current structure. This can be seen graphically by noticing that the slope of the line of the proposed structure is steeper than the current structure. ROE will also behave in a similar fashion. 11. The market value of No Leverage, Inc is determined by finding the net income for the company. Net Income can be calculated by EBIT * (1 - tc). Since these cash flows occur every year, no growth rate is assumed, and the full amount is paid to the stockholders as dividends, then the present value of the cash flows can be determined by valuing the cash flows as a perpetuity. To value the perpetuity, an appropriate discount rate is needed. In this case the discount rate is the cost of capital to the unlevered firm (Ru). Since this is an all equity firm the cost of capital equals the cost of equity.  EMBED Equation.3  b. Assuming M & M proposition I with taxes holds, the value of the levered firm equals the market value of an unlevered firm plus the present value of the tax shield. VL = Vu + Present Value of Tax Shield VL = $796,000=660,000+(8,160/0.06) No Leverage, Inc.High Leverage, IncEBIT $100,000  $100,000 Interest024,000Taxable Income10000076,000Taxes (34%)34,00025,840Net Income $66,000 $50,160Total Cash FlowsTo Stockholders $66,000 $50,160 To Bondholders024,000Total cash flow from assets $66,000 $74,160 OREBIT $100,000 $100,000Taxes (34%)34,00025,840Total cash flow from assets $66,000 $74,160Yearly tax savings $ - $8,160 PV of tax shield (r=0.06) $ -  $136,000  c. Market Value of Equity = Total firm value - Market value of debt Market Value of Equity = $796,000 - $400,000 Market Value of Equity = $396,000 When the effect of corporate taxes is considered, the value of the levered firm equals the market value of an unlevered firm plus the present value of the tax shield. d. High leverage has a fixed, perpetual level of floating rate debt so we can assume that the levering/unlevering relationship is best represented by Case 3. So the new return on equity is computed as follows:  EMBED Equation.3  The WACC for High Leverage, Inc. is a weighted average of the cost of the firm s debt and its equity adjusted for the tax effects of the debt.  EMBED Equation.3   EMBED Equation.3  So the APV valuation method previously used gives the same value as the FCF method once the return on equity (therefore the WACC) is adjusted for the different capital structure. 12. What is the incremental value of the proposed capital structure? To calculate the value of the proposed capital structure change we need to consider the tax shield of debt and the financial distress (bankruptcy) costs of the capital structure change. There are also the other effects such as agency issues and contracting costs but we dont have any information to directly estimate a value. We will deal with those issues in the discussion in part (b). First, we can compute the expected incremental cost of financial distress by taking the increase probability of distress (50%) and the cost of distress ($9 to $11 million). So the expected incremental cost of distress is between $4.5 and $5.5 million (0.5*9=4.5). To calculate the incremental after tax debt shield we need to compute the PV of the 8 years where the capital structure is different from todays structure. We need an r which represents the riskiness of the tax debt shield. Since the riskiness of the tax shield is stated to be similar to the riskiness of the firms business, the appropriate r would be the return on assets, 12%. To get the yearly debt tax shield flows we need to estimate the incremental cost of debt for each year then the corresponding tax savings (20% tax rate). Finally we discount these flows back to time 0 which gives us a tax debt shield of $5.05 million. Combining the tax debt shield and the expected cost of financial distress we have an incremental value of the new capital structure of a range between $-0.45 to $+0.55 (-4.5+5.05 and -5.5+5.05). 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Please refer to the lecture notes for a full listing of the other advantages and disadvantages of capital structure choice. Ill give some examples of advantages and disadvantages. On the plus side, debt performs a monitoring role which reduces managerial discretion and the free cash flow problem which lowers potential agency costs. Since this is an MBO, this leverage may signal that management knows that the cash flows of the company will be able to support this level of debt. On the negative side, this much debt significantly increases the likelihood of financial distress (50%) so there is a greater probability that the firm may underinvest (reject positive NPV projects). In addition, if the firm gets too close to distress, they may begin to risk shift (increase the riskiness of its investments to make that one big bet in order to avoid bankruptcy) which shifts risk to debt holders. In general, how will this proposed change in capital structure affect the shareholders expected return on equity? What will the new return on equity be in the first year of the MBO? What will the new return on equity be in the second year of the MBO? (Assume delta=0 for this part) In general we know that adding debt increase the riskiness of the equity holders. Since we know that the riskiness of the assets (business risk) is similar to the riskiness of debt, we can use Case 1 to represent the relationship between the returns on assets, equity and debt. The new return on equity in the first year is 30%.  EMBED Equation.3  The new return on equity in the second year is 20%.  EMBED Equation.3  The original return on equity is 12.67% (note and this will also be the return on equity for the firm again starting in year 9).  EMBED Equation.3  Based on the above information would you recommend the firm do the MBO? The numerical calculations show that the range of values for the MBO is close to zero (-0.45 to +0.55). Assuming an equal likelihood across the range of distress costs, we are slightly positive but this includes an assumption not provided in the problem. Based on the information given in the problem, the magnitude of the other advantages and disadvantages is difficult to assess. Since the equity portion of MBOs are owned by the managers of a firm (in other words, all of their money is on the line), Im willing to give a slight advantage to this MBO in terms of agency costs. Bottom line, the financing seems to be a neutral valuation consequence (NPV=0) or slightly positive. So my advice would be to proceed with the MBO if (and only if), the management change caused by the MBO unlocks value in the company.   PAGE  PAGE 1 seq _endnote \* ArabicError! 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